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A deal is expected to be announced sometime this week, possibly as soon as Tuesday afternoon, the source said.

According to the Financial Times, at least one of the bids surpassed $60 million, which is "a record sum for US presidential memoirs."

Both the former president and the former first lady are writing books about their time in the White House. The pair of books will be published separately, but publishing houses like Penguin Random House are bidding for the books together.

It is unclear when the books will come out.

Lawyer and literary agent Bob Barnett, who is representing the Obamas for the joint book deal, declined to comment. Obama spokesman Kevin Lewis did not immediately respond to a request for comment.

Former President Obama's past books were published by Penguin Random House. The FT said Penguin "is leading the pack for the Obamas' joint publishing deal."

Another publisher, Crown, reportedly paid about $10 million for the rights to George W. Bush's White House memoir.

Book deals are usually predicated on a publisher's expectations about sales. Books by the Obamas are virtually guaranteed to be best-sellers, selling millions of copies and generating weeks of media attention.

Book industry bidding wars get competitive for other reasons as well. The opportunity to be in business with a famous figure like a former president is a factor.